One problem with a “central” P-trap is that if it were done that way, you’re going to get nasty smells somewhere. Sewage frequently doesn’t make it out of your house as fast as you think it will and running water down the drain changes the air pressure in the drain line to varying degrees.

The main reason it’s positioned so close to the drain opening is to accommodate venting. Every drain opening has to be vented, typically with a pipe going through the wall to a vent stack in the attic, to prevent the P-trap from being sucked dry when you do something like flush the toilet or run the clothes washer.

Ever run the washing machine and hear a sink on the other side of the house gurgling during the drain cycle? That’s because the washer draining increases the air pressure in the sewer line and the sink isn’t properly vented causing air to bubble through the the P-trap.